How to construct an equilateral triangle using a pair of compasses

 

Step 1

 

Draw line segment AB, whose length is equal to a.

Как построить равносторонний треугольник с помощью циркуля

Construction an equilateral triangle using a pair of compasses. Step 1

Step 2

 

Take a pair of compasses. Put the fixed part of the compasses at point A and the moving part at point B. Draw a circle.

The length of the radius of the circle will be equal to the length of side (АВ–а).

Как построить равносторонний треугольник с помощью циркуля

Construction an equilateral triangle using a pair of compasses. Step 2

Step 3

 

Now put the fixed part of the compasses at point B and the moving part at point A. Draw a circle.

So, the length of the radius of the circle constructed will be equal to the length of the side (АВ – а).

Как построить равносторонний треугольник с помощью циркуля

Construction an equilateral triangle using a pair of compasses. Step 3

Step 4

 

The circles intersect at two points. If points A and B are connected with one of these points, a regular triangle will be constructed.

The triangle constructed will be regular, as all the sides will be equal in length to the lengths of the radiuses of the circles, which are equal to a.

Как построить равносторонний треугольник с помощью циркуля

 

 

Как построить равносторонний треугольник с помощью циркуля

Construction an equilateral triangle using a pair of compasses. Step 4